{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2023-10-05T11:22:11.292180166Z",
     "start_time": "2023-10-05T11:22:11.289872649Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "outputs": [
    {
     "data": {
      "text/plain": "<matplotlib.collections.PathCollection at 0x7f9cf0837730>"
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.ioff()\n",
    "x_v = [i for i in np.arange(-math.pi, math.pi, 0.1)]\n",
    "y_gt = [math.cos(i) for i in np.arange(-math.pi, math.pi, 0.1)]\n",
    "y_noise = [y_gt[i] + np.random.normal(loc=0, scale=0.4) for i in range(len(x_v))]\n",
    "plt.plot(x_v, y_gt, c='r')\n",
    "plt.scatter(x_v, y_noise, c='b')\n",
    "#plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-10-05T11:25:31.612693536Z",
     "start_time": "2023-10-05T11:25:31.572068997Z"
    }
   },
   "id": "7abde5376f8a4eb2"
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def EMA(seq: list, beta:float=0.9):\n",
    "    ret = seq.copy()\n",
    "    for i in range(1, len(seq)):\n",
    "        ret[i] = beta * ret[i-1] + (1 - beta) * seq[i]\n",
    "    return ret\n",
    "\n",
    "plt.plot(x_v, EMA(y_noise), c='y')\n",
    "plt.plot(x_v, EMA(y_noise, beta=0.5), c='m')\n",
    "plt.legend(['original', 'noisy', 'beta=0.9', 'beta=0.5'])\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-10-05T11:25:31.774007353Z",
     "start_time": "2023-10-05T11:25:31.708945477Z"
    }
   },
   "id": "b53ef55caa909633"
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false
   },
   "id": "16b95ae11309fb35"
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
